Rule: Q[10, 22]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $\frac{46189}{256}\cdot t^{10}-\frac{109395}{256}\cdot t^8+\frac{45045}{128}\cdot t^6-\frac{15015}{128}\cdot t^4+\frac{3465}{256}\cdot t^2-\frac{63}{256}$
• $P_2$:
  $\frac{46189}{256}\cdot t^{32}-\frac{3120472178377025215465125206927553}{2133012047099278755689871087616}\cdot t^{30}+\frac{34412844181058368755804678442404995}{6399036141297836267069613262848}\cdot t^{28}-\frac{8672732721989267493918603967920543915}{731623132155052613201625783052288}\cdot t^{26}+\frac{10207638064046921443198437973663456498125}{584566882591887037948099000658778112}\cdot t^{24}-\frac{10600960619059486898143342610976513752325}{584566882591887037948099000658778112}\cdot t^{22}+\frac{23264473077969551522908737410389302675}{1704276625632323725796206999005184}\cdot t^{20}-\frac{629643996607474718837893832171580822375}{83509554655983862564014142951254016}\cdot t^{18}+\frac{195359254476813554340929914128263925075}{63860247678105306666599050492135424}\cdot t^{16}-\frac{2135489098187760439394993422397159290125}{2362829164089896346664164868209010688}\cdot t^{14}+\frac{211660985049725866947746026970616262065}{1109872291479214814226866312890320896}\cdot t^{12}-\frac{62416389752995481435118511772898689804305}{2243051901079493139552496818351338530816}\cdot t^{10}+\frac{5983890020155421137219234203798692920425}{2243051901079493139552496818351338530816}\cdot t^8-\frac{27366109611983127248719567727664675}{176743511234693336975218408190949376}\cdot t^6+\frac{1514301476746971434003089333152615375}{320435985868499019936070974050191218688}\cdot t^4-\frac{18300318278210747643193190950410531}{320435985868499019936070974050191218688}\cdot t^2+\frac{36785056970127390811459471518867}{320435985868499019936070974050191218688}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.